Answer:
The volume of an aluminum cube is 0.212 cm³.
Explanation:
Given that,
Edge of cube = 4.00 cm
Initial temperature = 19.0°C
Final temperature = 67.0°C
linear expansion coefficient ![\alpha=23.0\times10^{-6}/C^{\circ}](https://tex.z-dn.net/?f=%5Calpha%3D23.0%5Ctimes10%5E%7B-6%7D%2FC%5E%7B%5Ccirc%7D)
We need to calculate the volume expansion coefficient
Using formula of volume expansion coefficient
![\beta=3\alpha](https://tex.z-dn.net/?f=%5Cbeta%3D3%5Calpha)
Put the value into the formula
![\beta=3\times23.0\times10^{-6}](https://tex.z-dn.net/?f=%5Cbeta%3D3%5Ctimes23.0%5Ctimes10%5E%7B-6%7D)
![\beta=0.000069=69\times10^{-6}/C^{\circ}](https://tex.z-dn.net/?f=%5Cbeta%3D0.000069%3D69%5Ctimes10%5E%7B-6%7D%2FC%5E%7B%5Ccirc%7D)
We need to calculate the volume
![V= a^3](https://tex.z-dn.net/?f=V%3D%20a%5E3)
![V=4^3](https://tex.z-dn.net/?f=V%3D4%5E3)
![V=64\ cm^3](https://tex.z-dn.net/?f=V%3D64%5C%20cm%5E3)
The change temperature of the cube is
![\Delta T=T_{f}-T_{i}](https://tex.z-dn.net/?f=%5CDelta%20T%3DT_%7Bf%7D-T_%7Bi%7D)
Put the value into the formula
![\Delta T=67-19 = 48^{\circ}C](https://tex.z-dn.net/?f=%5CDelta%20T%3D67-19%20%3D%2048%5E%7B%5Ccirc%7DC)
We need to calculate the increases volume
Using formula of increases volume
![\Delta V=V\beta\Delta T](https://tex.z-dn.net/?f=%5CDelta%20V%3DV%5Cbeta%5CDelta%20T)
Put the value into the formula
![\Delta V=64\times69\times10^{-6}\times48](https://tex.z-dn.net/?f=%5CDelta%20V%3D64%5Ctimes69%5Ctimes10%5E%7B-6%7D%5Ctimes48)
![\Delta V=0.212\ cm^3](https://tex.z-dn.net/?f=%5CDelta%20V%3D0.212%5C%20cm%5E3)
Hence, The volume of an aluminum cube is 0.212 cm³.